C# Class TriangleNet.Primitives

Check, if the three points appear in counterclockwise order. The result is also a rough approximation of twice the signed area of the triangle defined by the three points.

Uses exact arithmetic if necessary to ensure a correct answer. The result returned is the determinant of a matrix. This determinant is computed adaptively, in the sense that exact arithmetic is used only to the degree it is needed to ensure that the returned value has the correct sign. Hence, this function is usually quite fast, but will run more slowly when the input points are collinear or nearly so. See Robust Predicates paper for details.

Initialize the variables used for exact arithmetic.

'epsilon' is the largest power of two such that 1.0 + epsilon = 1.0 in floating-point arithmetic. 'epsilon' bounds the relative roundoff error. It is used for floating-point error analysis. 'splitter' is used to split floating-point numbers into two half- length significands for exact multiplication. I imagine that a highly optimizing compiler might be too smart for its own good, and somehow cause this routine to fail, if it pretends that floating-point arithmetic is too much like real arithmetic. Don't change this routine unless you fully understand it.

Find the circumcenter of a triangle.

The result is returned both in terms of x-y coordinates and xi-eta (barycentric) coordinates. The xi-eta coordinate system is defined in terms of the triangle: the origin of the triangle is the origin of the coordinate system; the destination of the triangle is one unit along the xi axis; and the apex of the triangle is one unit along the eta axis. This procedure also returns the square of the length of the triangle's shortest edge.

Find the circumcenter of a triangle.

Check if the point pd lies inside the circle passing through pa, pb, and pc. The points pa, pb, and pc must be in counterclockwise order, or the sign of the result will be reversed.

Uses exact arithmetic if necessary to ensure a correct answer. The result returned is the determinant of a matrix. This determinant is computed adaptively, in the sense that exact arithmetic is used only to the degree it is needed to ensure that the returned value has the correct sign. Hence, this function is usually quite fast, but will run more slowly when the input points are cocircular or nearly so. See Robust Predicates paper for details.

Return a positive value if the point pd is incompatible with the circle or plane passing through pa, pb, and pc (meaning that pd is inside the circle or below the plane); a negative value if it is compatible; and zero if the four points are cocircular/coplanar. The points pa, pb, and pc must be in counterclockwise order, or the sign of the result will be reversed.